A283980 a(n) = A003961(n)*A006519(n).

1, 6, 5, 36, 7, 30, 11, 216, 25, 42, 13, 180, 17, 66, 35, 1296, 19, 150, 23, 252, 55, 78, 29, 1080, 49, 102, 125, 396, 31, 210, 37, 7776, 65, 114, 77, 900, 41, 138, 85, 1512, 43, 330, 47, 468, 175, 174, 53, 6480, 121, 294, 95, 612, 59, 750, 91, 2376, 115, 186, 61, 1260, 67, 222, 275, 46656, 119, 390, 71, 684, 145, 462, 73, 5400, 79, 246, 245

Offset

1,2

Comments

Completely multiplicative since both A003961 and A006519 are. - Andrew Howroyd, Jul 25 2018

Links

Antti Karttunen, Table of n, a(n) for n = 1..10001

Formula

a(n) = A003961(n)*A006519(n).

From Michael De Vlieger, Dec 29 2019: (Start)

a(p_k) = p_(k+1) for odd prime p.

a(2^k) = 6^k.

a(p_k#) = p_(k+1)# for p_k# = A002110(k). (End)

Example

From Michael De Vlieger, Dec 29 2019: (Start)
a(1) = 1 since 1 is the empty product.
a(2) = 6 because 2 = 2^1 in form p_k^e; switching p_(k+1) for p, we have 3^1 = 3, and the largest power of 2 dividing 2 is 2^1 = 2; thus 3 * 2 = 6.
a(4) = 36 since 4 = 2^2 -> 4(3^2).
a(6) = 30 since 6 = 2^1 * 3^1 -> 2(3 * 5).
a(12) = 180 since 12 = 2^2 * 3 -> 4(3^2 * 5) = 4(45) = 180.
a(30) = 210 since 30 = 2 * 3 * 5 -> 2(3 * 5 * 7) = 210.
(End)

Mathematica

Array[(Times @@ Map[#1^#2 & @@ # &, FactorInteger[#] /. {p_, e_} /; e > 0 :> {Prime[PrimePi@ p + 1], e}] - Boole[# == 1])*2^IntegerExponent[#, 2] &, 75] (* Michael De Vlieger, Dec 29 2019 *)

Prog

(Scheme) (define (A283980 n) (* (A006519 n) (A003961 n)))
(PARI) a(n)={my(f=factor(n)); prod(i=1, #f~, my(p=f[i, 1], e=f[i, 2]); if(p==2, 6, nextprime(p+1))^e)} \\ Andrew Howroyd, Jul 25 2018
(Python)
from sympy import nextprime, factorint
from math import prod
def A283980(n): return prod(nextprime(p)**e if p > 2 else 6**e for p, e in factorint(n).items()) # Chai Wah Wu, Dec 08 2022

Crossrefs

Cf. A003961, A006519, A283477.

Sequence in context: A070399 A137763 A029763 * A288211 A038259 A358590

Adjacent sequences: A283977 A283978 A283979 * A283981 A283982 A283983

Keyword

nonn,mult

Author

Antti Karttunen, Mar 19 2017

Status

approved